We have long wire with constant charge density that is put inside a grounded metal housing with a shape of cylindrical section (a ≤ r ≤ b and 0 ≤ ϕ ≤ α). We need to find potential inside the box. 

Relevant equations are:

Δf=-(μ/ε0)*∂^2(r), where μ is linear charge density [As/m], ε0 is Vacuum permittivity, f is the potential (Δ is laplace operator) and ∂^2(r) is two-dimensional delta function.

f (a ≤ r ≤ b and 0 ≤ ϕ ≤ α) = 0. 

Green's function for ΔG =∂^2(r-r0),two dimensions and no boundary conditions: G(r,r0)=(1/2*pi)*ln|r-r0|

I am trying to solve the problem with green's function since it seems that solving this problem with separation of variables is too complicated.



 

1 hour ago, t38 said:

I am trying to solve the problem with green's function since it seems that solving this problem with separation of variables is too complicated.

Do you have to use Greens?

 

Separation of variables is easy with this Laplace equation.

 

I presume one of the boundary conditions is potential, V = 0 at the cylinder?